Xcode Keyboard Shortcuts Conflicted
I had this problem too, and nothing in Keyboard Shortcuts in System Preferences was showing "^-6" as bound to anything.  But I figured it out...


Activate Mission Control
Add a bunch of spaces (I added 5, so I had 6 total [not counting Dashboard])
Go back to Keyboard Shortcuts. You should now see the "Switch to Desktop n" options there under the Mission Control heading
Uncheck them
Reactivate Mission Control and remove the added spaces