Don't know about the 310RL, but both of our sinks have "air admittance" valves under the sink. That provides the venting for the drain. We had some odor problems and I replaced the factory ones with the Studor Mini Vent https://www.lowes.com/pd/Studor-Mini-Vent-Air-Admittance-Valve-with-PVC-Adapter/1000604287
This should screw directly onto the vent pipe under the sink without any modifications to your piping. They work great and no more odor.