It's not the size of the bolt head that you need, it's the size of the actual thread and it's pitch i.e. M6x1.2
To insert a helicoil you first need to prepare the damaged hole, it requires you drill out the damaged thread and over-size slightly, you then tap a larger thread into the hole by hand and then you can insert the helicoil. The helicoil itself is your new thread.
To decide how much to drill it out by and what size helicoil you need, first find out what size bolt it is for the housing. Should be quite easy as you have the bolt at hand.