Keyboard Shortcut for moving left/right a space doesn't work
This helped me: 

https://discussions.apple.com/message/18340925#18340925

Paste this into Terminal (it's all one line, not two):

mv ~/Library/Preferences/com.apple.symbolichotkeys.plist ~/Desktop/com.apple.symbolichotkeys.plist

Press 'return'.
Log out and log in to your system.
Go to System Prefs and set up your hotkeys as you want.