Probably mid 1950's...but before 1958
Welcome to the Forum from Virginia.
S&W started stamping Model no's in the yoke area in 1958 so your gun is earlier than that probably. The Standard Catalog of Smith & Wesson, 4th Edition lists 32 Long revolvers with serial numbers 536685 as 1946 to s/n 712953 in 1960. Sorry...but that is a wide range covering 14 years. You would need to send for a Letter from the SWHF (Smith & Wesson Historical Foundation) to find out exactly when and where your revolver shipped.
As to value, I have seen them go for $400 to $750 around here, of course depending upon condition and whether any accessories were included (box, documents, tools, etc.).
My Model 31-1 shipped in September 1975 and was purchased at a local gun store in October 1975. I bought it at an estate sale after the original owner passed. The gun was unfired, the heirs never even knew the woman owned a gun, and in the box with the gun and documents was the original sales receipt.
The local gun store is now a physical Interstate highway exit ramp!!
I would say that your gun with fake plastic grips and average condition with slight bluing wear on high spots, but otherwise good mechanical condition would be in the $400 to $450 range.
Post some pictures if you can. We love pics and if you are interested in selling, there is no better place than this Forum, Guns for Sale sub-forum. You will get a fair price for sure.
Good luck with your gun.