My main drainage line is clogged about ten feet below the basement. I have been snaking the line but it seems to be hitting something solid. I also have been adding a drain solution to dissolve the blockage but it seems to not be doing much. The water in the line is black and filled with sludge. I really don't know what else to do. Can you help?

Rent a power sewer auger unit instead of doing this by hand. Rent one with several different heads including a cutter. Stop with the chemicals for now.

Bob's correct,

Rent a sewer machine ,(see image) from your local rent-all place. Make sure the furnish you with a cutter tip, ( see image) to cut through any roots that may be blocking you and a auger tip,(see image) to drill into and bring back any obstruction. Where are you snaking from? City sewer or are you on a septic tank? Good luck and let us know what you find. Tom