A few checks……
Assumption, having two speakers means stereo unit?
Is there a mono/stereo switch…if in stereo fm is is stereo or mono sound therefore sending a signal to both speakers?
Is the TT plugged into a phono input on the rear of the unit, or integrally?
If on the rear try switching the plugged in RCA connectors, if a bad wire sound should move to the other speaker.
After that test, you need to check continuity from the cartridge to the farthest accessible end of the wires. If plugs in the rear that is the RCA connectors. But if its inside that is a more difficult point(s) to locate.
For these continuity test you need an Ohmeter, do not at this time disconnect the cartridge which looks like its soldered?
Anyway, I would lift out the TT to access the bottom…cautiously because I can’t see how the connections are underneath, they could be long or short wires. SO, if you can access under check wire runs from whatever is there to the cartridge …..if a wire has been broken between the cart and the check points that will pin down one of the hot, L or R wires is broken. The common ground is ok otherwise neither channel would work.
If you can do the wire check and all is good, there is probably only two places where there is a break, inside the stereo unit, or inside the cartridge .
You can check the cartridge two ways, unsolder or remove the wires from the cart body and check continuity thru the body, or cut the wires where you can, strip the wires, and check thru the cart body, each channel pair of wires should complete a circuit if you can determine which is common ground, after finding one wire run is broken, careful you don’t assume the ground, you repair the broken wires and continue. If there is a broken circuit thru the cart, then the cart is bad.
You need to check as many possible wire runs as you can before making any assumptions.