Did the landlord provide you with the manufacturer's user manual? Did you have a duty to read it?
If not, was it your duty to acquire the manual?
Does the manual give any warnings as to placing muddy towels or something equivalent? Were you on notice of a particular limitation?
Would a reasonable, prudent person know or should have known that the muddy towel would have caused the damage that resulted?
Were there any intervening factors? i.e., How old was the washer? Was it near or past its warranty? Was it near or past the industry's average useful life?
Would it have broken anyway washing a non-muddy towel?