According to Rem records your M/6 was made in 1925. If so, it will have a date code that will tell you the month/year of production. Unfortunately, Rem records for the M/6 were "Reconstructed" at a later date from the best info they could find. M/6 serial #s have been found that are 50,000 higher than the records show. Your date code could be on the bottom of the barrel just ahead of the fore-arm. The key can be found on the home page of this site.
We do not attempt to give a value on rifles we can't handle, but I wouldn't get your hopes up for getting much of a shotgun in an even trade.