Do you mean that the video data cable from the back of your computer disappears into the structure of the monitor?
Does the "break" seem to be close to, or inside the monitor - give it a gentle wiggle.
If you are going to replace this cable yourself you are going to have to do some careful surgery to be able to disconnect the old.
With luck the cable will have failed at or close to the monitor which is where most strains and wiggles happen in use.
So if you have enough cable to cut off the bad length it is just a careful task to reconnect each conducting lead in turn.
You might find that a local repair shop would chop one from a defunct CRT for you. At least in this TFT repair you don't have dangerous residual voltages to worry about while working at it.