Albert's comment and link is a useful starting point. I happen to have not only the LP from this program, but also a video tape made from the kinescope recording of this 1957 broadcast. The last time I checked on this recording, I don't think the LP was worth a lot, except maybe to a given collector who wants to acquire it. The audio quality of the recording isn't that great, so the recording has mainly historic merit.
If you want to sell the LP, you might check the "Goldmine" LP listings to see if you can find a general value for the LP based on its condition.
Interestingly, you may have an easier time selling the LP -- and get a lot more money for it -- if you market the LP in Japan. Japanese collectors often like to acquire American jazz recordings from the 1950's, although they are no longer paying the incredibly high prices for LP's that they did 10-15 years ago before the Japanese economic bubble burst.
If I were going to sell my LP copy of this recording, I'd probably price it at $50-75 and see if I got any takers.