AR-XA turntable cable question

Hi, recently got an AR-XA turntable, and have a cable problem. One of
the RCA input cables had a very funky connector, so I decided to
replace it. Once I cut the cable, and was going to use a gold RCA jack
replacement from Radio Shack, I noticed that the turntable cable had
three wires, a central core, which I assume is the signa main for that
channel, another wire, which I assumed was the ground, and a third
wire, which surrounded the signal wire, but was outside the insulation
of the main (another ground?). The RCA jack replacement has a main
connection, which goes to the pin, and a place for the ground
connection. My question is, should the two ground wires be connected
together, and attached to the ground of the RCA jack, or should one
simply not be connected to anything? I am having trouble getting it
correct, and keep getting a hum. Is this something idiosyncratic to
the AR turntable, or is this how turntable cables work? There is no
separate ground wire, as there is on my Dual turntable. Thanks, and
sorry if this is an elementary question. I was going to take it in to
get repaired, but it seems awfully rudimentary, and I can use a
soldering gun...

.

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