Landlord or tenant responsibility?

hello, i rent a house and i have a problem . i have a clog somewhere in my pipes. The kitchen sink got backed up(standing water..i tried a plunger, drain cleaner removed the trap and i even bought a 15ft drain snake and tried to unclog it without any luck. After talking to a few people they said that it could be the vent and the airflow isnt venting right or it is deeper in the pipes..and they told me it would be the landlords responsibility. I live in NC whose responsibility is it? mine or the landlords? i have tried to unclog it and i did not purposely clog it? i personally cant afford a plumber either...please advise thanks!