Least destructive way to run a cable through metal double doors

[Hal65]

I have somewhat of a strange setup with my main room and bedroom being separated by heavy metal double doors that don't slide very well:

 

 

This image is mirrored and should be reversed left to right.

 

The TV cable has been wired to go into the side of the metal frame and come out into the wrong room (the main one). This is an issue because if I have a Thai girl over I want that door closed to block light (for her) and TV noise (for me). Right now I have to keep it cracked open to run the cable through.

 

What is the best way to get the cable into the other room using a small hole? Drilling the metal frame, the drywall, or something else?

 

Edited June 8, 2017 by Hal65

[regedit]

Drill 2 holes, 1 from each side of the frame,  into the wall,  at an angle so that they will both meet. Then feed cable in and through. Might need to finish with a 12mm drill bit. If cable doesn't easily feed in, use a length from a metal coat hanger to lead the way.