I am unable to pair my iPhone 11 Pro Max with my Apple TV

I assume you have an Apple TV 4 HD or Apple TV 4K. Remember to sign in with same Apple ID om both devices.

On your Apple TV go to:

Settings -> Remote controls and devices -> Remote controls and devices.

Hold your iPhone close to your Apple TV. Then should your Apple TV pop up on your iPhone, press Connect and enter the code that appears on your Apple TV.

Now your iPhone and Apple TV should be connected. You can e.g. use your iPhone as Remote. If your Apple TV does not show up on your iPhone, make sure Bluetooth is turned on and that both devices are on the same WiFi network.