​Gloria Estefan: Caught by the rhythm

Singer Gloria Estefan.

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The 1987 hit "Anything for You" by the legendary Gloria Estefan is now ON BROADWAY. A new musical based on her life is currently in previews. Her path to center stage wasn't always an easy one, as she tells our Lee Cowan:

Back in the '80s, few knew what "Latin crossover" really meant in music, until this happened:

Gloria Estefan and the Miami Sound Machine became one of the decade's signature sounds.

It's no easy feat to make the conga more than just a wedding reception ritual. But Gloria did that, and much more.

She was polished, poppy, and popular. She's had more than 100 hits across the Billboard charts, brought home seven Grammys, and sold more than 100 million albums.

These days, Estefan is at a different stage in her life, literally. At 58 the Queen of Latin pop is seeing her life turned into a mega-watt Broadway musical, "On Your Feet."

"Is it what you expected?" Cowan asked.

"I don't think I ever could have imagined what this was going to be like," she replied. "I never would have imagined it would be so emotional."

"It's very personal."

"Oh my gosh, so much so."

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Gloria Estefan's first meeting with Ana Villafañe.
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She's played by actress Ana Villafañe, who bears an uncanny resemblance to Estefan, who recalled, "The minute she walked in, it was one of those 'movie moments,' like you know when they kid around in the movies, they say, 'That face! I must have that face!'"

They talked, and soon found out they had a lot more in common. She and Gloria both are Cuban-American, both grew up in Miami, and -- get this -- they both went to the very same Catholic high school (a few years apart, mind you).

"I remember Gloria coming to visit school," Villafañe said, "when you did the children's book 'Noel's Treasure Hunt.'"

"Yes! You were here for that?"

"Oh yes, and fun fact, I walked to where we are right now and there was a table and I was with my mom. You signed a book for me. I've never told you that!"

During a recent visit to their alma mater, the music made the years between them fade away. There they were, two products of immigrant families who had gone on to make it big.

"It really irks me when I hear someone say that the American Dream is dead, because that cannot be further from the truth," Estefan said. "This is one of the few countries in the world that doesn't put limitations on you. Only you put them on yourself. If you're willing to work hard, and persevere and follow your dreams and your passion and get ready to get a lot of no's and find your way around those no's, this is the dream place to do that."

Her partner in that dream is the only man she ever dated: her husband, multi-Grammy-winning producer Emilio Estefan.

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Gloria Estefan and Emilio Estefan, with correspondent Lee Cowan.
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He told Cowan the very first thing he noticed about Gloria was her eyes.

"Yeah, I love her eyes. I still love her eyes, almost 40 years after," he said.

The play begins (as they did) as young Cuban immigrants fleeing the regime of Fidel Castro. Gloria and her family were among the first wave of exiles to arrive in Miami, settling into a tiny apartment.