She may be one of the most famous A-listers in the world now, with an adoring six kids and a husband who makes her the envy of most women in America, but there was a time when Angelina Jolie, 36, was just a troubled young woman who got caught up in the limelight too quickly.

"I went through heavy, darker times and I survived them," Jolie told 60 Minutes. "I didn't die young, so I'm very lucky. There are other artists and other people who didn't survive such things."

It's been an uphill battle for Jolie, from her telling breakout portrayal of drug-addicted model Gia Carangi in HBO's acclaimed 1998 film, Gia, and her subsequent, often-bizarre marriage to actor Billy Bob Thornton, 56, which at one point saw the duo wearing vials of each other's blood around their necks, to being received as a respectable actress, professional mom and active humanitarian.

Though Jolie, the daughter of actor Jon Voight and Marcheline Bertrand, realizes she was lucky for surviving the brunt of her own self-destructive impulses, she still acknowledges a dark streak in herself. "I'm still a bad girl," she added. "I still have that side of me. It's just in its place now…. It belongs to Brad."

You can see the full 60 Minutes interview with Jolie on CBS, Sunday at 7 p.m.

In the meantime, watch a clip here:

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