"I like tomatoes."
So if I say I don't like tomatoes, that would just require adding "Nie" right? Nie lubię pomidory.
no. it also needs change is cases, accusative->genitive.
Lubię pomidory- nie lubię pomidorów.
Genitive has many functions. Apart from possession (like "George's car" or "the house of the headmaster") it also is needed when you negate a sentence that took Accusative. Note that only Accusative changes the case when negated.
If you liked "these" potatoes, it would make sense - more sense even, probably.
But as "podobają mi się" implies (mostly) an aesthetic impression, it sounds like a rather strange thing to say that you think "tomatoes are generally aesthetically pleasing and seem like they will be tasty". Not all of them are, although some specific ones can be.