This TV does have Digital Audio Out port to connect headphone base unit with an optical cable.
Please make sure optical cable isn't internally broken, and plugged securely and tight in TV and headphone base unit.
Select Optical input in headphone base unit.
Now it needs to make some change in TV setting menu to enable optical output port but this will mute the TV speakers...
Use the Quick Settings screen to change to the connected device: Use the Select button to select Audio Out/Optical on the Sound Output menu. Settings > up directional button > Sound Output.
OR go through following procedure...
Use the Settings screen to change to the connected device: Select Audio Out/Optical on the Sound Output menu. Settings > Sound > Sound Output.
If you watch only cable channels then it would be best to connect the headphone base unit to Audio Out jacks on cable box, this way you will keep getting sound from TV speakers.
Please reply back with the result