Huma Abedin on overcoming her husband Anthony Weiner's betrayals

Huma Abedin's story is as unlikely as it is extraordinary, from the pinnacles of power as a top aide to Hillary Clinton, to the depths of public scandal as the wife of disgraced former Congressman Anthony Weiner.

In her first-ever television interview, she explained to "CBS Evening News" anchor and managing editor Norah O'Donnell why she is speaking out now: "Well, I think for most of my adult life, certainly in the last 25 years that I've been in public service or in the public eye, I have been the invisible person behind the primary people in my life. But what I realize [now] is that, if you don't tell your story, somebody else is writing your history."

In new book, called "Both/And" (published by Scribner, a part of Viacom/CBS), Abedin writes about a life lived in many worlds. Born in America, she was raised in a sheltered Muslim environment in Saudi Arabia. Her mother, from Pakistan, and her father, from India, were both professors and Fulbright scholars who traveled the globe.