The first thing you've got to do is educate your client. Chewing gum is not something you get off only when you get the carpet cleaned, it's something the cleaners should do on a daily basis. We stopped doing chewing gum many years ago for that reason and it worked, we kept the business, the cleaners were ordered to remove it every day and the premises were free of chewing gum, permanently, one brewery chain even thanked me for having solved the chewing gum problem for them.
From a cleaning perspective you have to be aware that because of the high traffic in these kind of places the carpet could well be choked pile deep with dust and grit and the moment you clean it it could turn black, especially in the doorways and traffic lanes. If so, you've got a nightmare on your hands and it is really difficult to sort out once that happens. If they have the carpets cleaned regularly you could be ok, but if it's been years then I would be tempted to leave it well alone. The trick with this kind of work is knowing which ones to walk away from and which to take on.
Simon