Give up on the idea of a drone being able to lift the extra weight of a high current supply cable, its
not going to happen.
11A at 3.7V is about 0.3 ohm load. thus the wires should be at most 0.03 ohms, which for 10m length
would mean perhaps 2kg of copper or aluminium in the cables...
Low voltage power doesn't travel long distances without stupidly thick cables. The only hope for tethered
flight is to send the power at a higher voltage and buck-convert on the rotorcraft - a high power buck converter
may weigh a lot more than the LiPo battery.
So the correct approach is to fly from battery, and tether using fishing line, or spectra/dyneema kite line, which is much much lighter.