No, the pull ratio on the 11 speed derailleurs is different so it won't work, even if you ignore the extra gear. You can probably pick up a GS cage 10 speed 105 or Ultegra derailleur on ebay pretty cheaply.
Other options are:
11 speed shifter, cassette and derailleur (you don't need to change the crankset, front derailleur or shifter, they'll be fine).
Smaller chainrings (6600 is 5-bolt though so this will likely mean a new chainset).