My daughter got gum stuck in her hair the other day when she fell asleep with it in her mouth (I thought that was a myth, but it really does happen). Since she was out for the night (yes, I'm a bad parent and she had sugar free gum right before bed), I decided to wait until morning. It wasn't at the end where it could easily be cut, it was right by the root, and in a lot of hair. Ugh!
The next day I grabbed some olive oil (we were camping), and put some on my fingers and rubbed it in her hair. Just to see if it was working i tried to remove some of the gum with my fingers, and it seemed to be coming out ok. I put more olive oil on the area, and all of the gum pulled right out of her hair! Not in one bunch, but in several passes pinching my fingernails together. If one had a comb and olive oil combo, it would work like a charm.