Brian , Like Zen said it could be 6mm or 8mm. I can't imagine you breaking a 8mm stud( 13mm nut) . You didn't say what size the nut was. Also like Zen stated ,over the years cases got swapped around and if you changed styles of coolers(doghouse to straight vertical) there was a stud that was furnished 6mm on one end and 8mm on the other end and you just "flipped " it over to fit whatever size case hole you had. You also have to pay attention to what style of seals you use. There is a set of cooler seals that are bigger on one side than the other. I don't know what you are dealing with, so I can't tell you what to use. If you have one of these dual threaded studs with the 6mm into the case and 8mm nut its no wonder it "popped" They are very tender.
There are a lot of folks that get these cominations of cooler-v-case wrong. I know of at least 3 styles of coolers from 1961 -1970. May be more.They will all work if you have the right kind seals and hardware.