TWL is correct. The difference between single-ended and balanced is indeed +6db. The same thing would happen if you switched from single-ended to balanced between your preamp and amp.
You never know what today will bring
I introduced new XLR Discovery Essence Interconnect in between my CDP and Pre today, in place of an older pair of very short audioquests with RCA termination. My speakers now deliver the same number of dBs as before with the preamp set two clicks LOWER. I did not expect such a substantial change in SNR. My thought is that this is due to balanced circuitry, not to differences in cable.