No, your turntable is grounded, as is with cheap turntables, the shield of audio signal is alteady the ground. They connected it inside.
What you hear is likely rumble.
Can you place the stylus on the lp in the grove, but do not turn the motor on. Do you still hear the hum? Measure how much mV or uV on phono output.
Then use test record with empty groves, measure hum again, compare.
This is best way to find out where the hum is comming from. If its mechanical from lousy spindle or motor vibration, it will be hard to fix.
