Why not specifically put in one price for cleaning the carpets and an additional charge for the cleaning of the gum?
That way you draw attention to the problem and the time consuming nature of removing it. Then if the potential client is getting quotes it firstly explains your pricing and the potentiL client has the option of going for just a cleaning or the bells and whistles approach of cleaning and chewing gum removal.
Secondly the potential client can then ensure whatever quotes he gets can at least be compared on a like for like basis.
Your competitors will either quote an all price which may look expensive in comparison or if their quotes are cheap(er) then the client can start asking awkward questions of the potential competitor..
Either way you either get an easier job or alternatively you get the job and a proper price because the client has made an informed choice of cleaner rather than simply going for the cheapest , unquantifiable price
Rog