yes the "dump" in public is the best place to take it.. if just a few cartons, you can cut them up and put in a regular trash bag and they take it but if a large quantity as you mentioned, the dump is better.. if you are a homeowner, by chance, you get a card to use at the incinerator center so there is no charge.. if you are not a homeowner, perhaps ask someone who has a card to go with you...
here is the most recent info I can find on hours:
For professionals:
• Monday-Friday 6am-11am
• Saturday 6am-10:45am
For taking garden debris and large objects:
• Monday-Friday by appointment 6am-11am
For individuals:
• Monday-Friday 6am-11:45am
• Saturday 6am-10:45am
There is someone on-site on Sundays and holidays for individuals to take only for household trash or separated glass and metal for recycling from 8am-11am