As other have commented, there is no sure way of avoiding damage or interference when the antennas are in close proximity. But there are a few things you can do to minimize the chance of interference.
Place the Ground Plane 180° From the Front of the TV Antenna
By placing the ground plane antenna in the opposite direction of the primary gain lobe of the TV antenna, the amount of signal from your VHF/UHF transmitter that is coupled into your TV antenna system will be minimized. The Friis equation helps to estimate the effect:
$$P_\text{rx}=P_\text{tx}G_\text{tx}G_\text{rx} \left(\frac{\lambda}{4\pi D}\right)^2 \tag 1$$
where Prx is the power in watts received by the receiver, Ptx is the power of the transmitter in watts, Gtx is the linear gain of the transmitting antenna, Grx is the linear gain of the receive antenna, $\lambda$ is the wavelength in meters, and D is the distance between antennas in meters. Note that the antennas cannot be in each other's near fields. This can be largely avoided by separating the antennas by at least 1 wavelength (2 meters).
To convert dB gain or loss to linear gain or loss:
$$G_\text{linear}=10^\frac{G_\text{dBi}}{10} \tag 2$$
If we assume that your ground plane antenna has a 2 dBi gain, the back end of the TV antenna has a -10 dBi gain, 5 watts of transmit power on two meters, and the distance between the antennas is 6 feet, formula 1 tells us that the power in the receive antenna will be 6.32 milliwatts. That is the equivalent of being within 1470 feet from a 15,000 watt ERP VHF television station with a 5 dBi gain TV antenna pointing directly at the TV station. That is a lot of power!
You can see from equation 1 that doubling the distance between the antennas, the received power is cut by 75%. Thus placing your antenna 12 feet from the TV antenna would result in 1.58 milliwatts at the antenna.
Avoid Using TV Antenna Amplifiers
TV antenna amplifiers are, by necessity, very wide bandwidth amplifiers. The power received from your ground plane antenna could cause IMD (intermodulation distortion) within the amplifier which could affect the desired TV signals.
Use Less Transmit Power
VHF and UHF stations primarily rely on line of site for communications. You may find that you can easily talk into a nearby repeater with a few 100 milliwatts. This will greatly reduce the possibility of interference with the TV system.
Use a Directional Transmit Antenna
A small VHF/UHF Yagi pointed away from the TV antenna could add 10 dB or more of path loss to the signal that gets coupled into the TV antenna. The practicality of this solution depends on the direction of the repeaters or other hams with which you wish to communicate.