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Letterman may need to win back female fans

David Letterman may owe an apology to his legion of female viewers.

The late-night-TV king appears to have weathered the storm from the revelation that he’s slept with female “Late Show” underlings, but he still has damage control to do.

“The men I’ve talked to think, ‘How could a person within your own company kind of betray you like this?’ ” said NBC News anchor Ann Curry.

“But the reaction I’m hearing from women is completely on the other end. They’re saying, ‘How could you have affairs . . . with members of your own staff?’ ”

Still, industry experts said Letterman’s infidelity likely won’t do lasting damage to his career.

“The only way this is a problem is if this snowballs, if some other crazy stuff comes out,” said Brad Adgate, director of research for Horizon Media.

CBS would have a tough time taking action against Dave since network boss Les Moonves dumped his wife for the much younger Julie Chen.

“You have Les Moonves sleeping with Julie Chen while he’s married, and you have Dave sleeping with this woman when he’s effectively married,” said Bill Gorman, of TVByTheNumbers.com.

“What’s the difference?”

david.li@nypost.com