This sixth sense would have to be at the same strength of your other senses. I do believe it is possible, but I haven't met anyone with a sixth sense that was not an animal.
For example, dogs and cats do have a sixth sense. They can normally tell when someone is about to die. In a nursing home they have a dog who runs around the grounds. The nurses can tell when someone is about to die because the dog runs into that persons room, sits there, and stays with that person all day. The dog attempts to comfort the soon to be dead.
Some claim dogs have this ability through smell, but others think it is a sixth sense.