On a carpet clean in a town centre bar the other day I found that simply spraying a bit of spotter on the wads and then scraping it with the lips of my hand tool was breaking it free. Then it was just a case of blasting the remains with really hot water (heated to about 90 in-tank), applying a bit more spotter, agitating with a handi groomer, then a final rinse and it was gone.
Working on about 3 or 4 wads at a time I got through about 25m² of really badly gummed carpet in about 45 mins. I was pleasantly surprised but the bar owner was gobsmacked! He thought he was "stuck" with it (scuse the pun)
He paid on the spot and gave me a tenner tip, two unheard of occurences in one go from a bar owner!
I've never really bothered with gum before, because of some of the reasons already mentioned here recently such as solvent damage, agitation damage and non-effectiveness of certain gum removal systems. But this was a real eye-opener for me.
One thing I noticed was that if I first tried rinsing the wads with hot water, it just made them go into a bigger gooey mess. Spotter, scrape off with hand tool lips, then deal with the residue seemed to be the best way to go.