Hair dilemma - can you help?

I have long hair down to my ankles but one side of my hair has become matted so badly that it has tangled to a tight knot which has to be cut off to my chin. I still have half a head of long hair on the other side and do not want to cut it. Can anyone suggest what I can do to make both sides blend in. I have been thinking about hair extensions but do not want anything which will pull out my existing hair from the roots. Which methods will allow me to grow my hair without any trauma?