It's disappointing that you would suggest cheating before, I don't know, TALKING to the partner. Sex is a healthy component to any relationship & life, I imagine if someone has been declining sex for an extended period of time there's more to this story.
I would suggest having an honest conversation with your partner about your feelings and needs (in a secure, non-threatening way) and asking why they aren't interested and what you can do to help. Perhaps seek couples therapy. If nothing else, you may find that they're open to a less monogamous marriage.