What you are describing in your cat is most likely gingival recession. You may also notice that under the gum where the root of the tooth is located, it may look a little bigger than the same tooth root on the other side.
Cats are very prone to dental disease related to gingivitis (inflammation of the gums). Once bacteria get into the pocket between the gums and teeth it causes a breakdown of the "periodontal ligament). The deep tissue that holds your teeth to the gums. Once this ligament breaks down the gingiva will pull back exposing more tooth and tooth root. The root of the tooth has less protection from bacteria and infection than does the "crown" or tooth above the gumline. So once the gingiva recedes you are starting down a path of tooth loss.
I would recommend making an appointment with your veterinarian and having your cat examined thoroughly. Some forms of dental disease can be related to an underlying body wide disease. They can make a recommendation for at home care or if your cat needs surgical dental treatment.
It is very common in cats to have tooth root death and then breaking off the crown of the tooth. It is very painful. Dogs and cats do not express dental pain the same way we do. They must keep eating and will tolerate the pain more than they should.
At home you can try brushing you cats teeth with a toothpaste made for cats/dogs. Human toothpaste has too much fluoride for dogs/cats.
Try a damp cloth with the paste and gently rub it along the outsides of the teeth. Sometimes just letting them initially lick the toothpaste will make them accept the process better.
I hope this has answered your questions, if not please let me know.