A brief look at your manual it does seem to have transmitting option, this from page 102 of your manual:
Listening to the TV through Bluetooth devicesSettingsSoundSound OutputBluetooth Speaker ListYou can connect Bluetooth audio devices to the TV. They must be paired using the TV's Bluetooth function. For more information on pairing, refer to the Bluetooth audio device's operating manual."This function may not be supported depending on the model or geographical area."If the TV fails to find a Bluetooth audio device, place the device closer to the TV, and then select Refresh."When you turn on a paired Bluetooth audio device, the TV detects it automatically, and then displays a pop-up window. Use this pop-up window to activate/deactivate the Bluetooth audio device."The sound quality may be affected by the condition of the Bluetooth connection."Before using a Bluetooth audio device, refer to “Read Before Using Bluetooth Devices"
Maybe one of the devices like Bradymartin suggested would be worth a try.