Swann Galleries has a copy of the first impression Return of the King up for auction in their Fine Books & Manuscripts auction on Nov 17, 2020 at 12:00PM ET - Sale 2551
8vo, publisher's blue cloth stamped in gilt, slight lean; unclipped dust jacket, fold corners nicked, head and foot of spine panel with small chips and short closed tears with associated creasing, lightly rubbed; contents including folding map clean and unmarked. First American edition. Boston: Houghton Mifflin Company, 1956
Estimate: $400 - $600 [Editor's note - seems a bit high to me]