I agree, you have an older model Rem. M11. It is a Browning design recoil operated auto-shotgun. Generally, the difference in this gun and the Browning A-5 is no magazine cut off lever and the safety type and position.
It should shoot well. I'm not sure if it had the recoil sleeves like the A-5 where the position of the two sleeves were different for light vs. heavy 2.75" loads? It probably does. In the old A5s there was a small paper schematic showing the correct position for the brass/steel sleeves glued inside the foreend.
"Nothing wrong with a little shooting as long as the right people get shot."
H. Callahan, Magnum Force 1973