You will have to get a HDbaseT balun set. It will essentially turns a single network wire into a long HDMI cable. Receiver end at TV, transmitter end at cable box. The cable box will have to sit in the utility room. Many HDbaseT have IR (for remote control) emitters and receivers and that signal is transmitted down the same network wire.
These are the ones I use for my clients.
http://www.wyrestorm.com/catalog/EX-70-4K
The other options are to fish a HDMI cable to the wallplate or mount cable box on shelf underneath.