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Television personality Dick Cavett is listing his beachfront estate on Long Island’s East End for $62 million. “After 50 years here, it’s the hardest thing in the world to do,” he wrote in an email. “I’ve loved every day here, but now it’s time to open a new chapter.”

Located in Montauk on Long Island’s Eastern tip, the shingle-style house—which Mr. Cavett painstakingly rebuilt after a 1997 fire—sits on roughly 20 acres on a bluff…