Soldering Cardas interconnect cables

Hi,

Need some help on soldering the Cardas Cross interconnect cables to the RCA plugs.

After I cut away the rubber shielding, the center core has 4 sets of cables - colored in white, green, blue and black. Just outside this set of 4, there are a few strands (copper) that goes round this set of 4 and then just underneath the external brown rubber there are a larger strand of copper cables.

Do I solder the set of 4 into the inner pin of the RCA and the external strand of copper (just beneath the brown rubber) on to the external shell of the RCA plug?

I did that and the sound through the cable was very soft. Anyone knows whats wrong or am I doing it wrongly?

Thanks for any heads up!!