If the other person never opens to caring conflict resolution, then you need to decide for yourself how to take loving care of yourself in the face of the unresolved conflict. This means accepting your helplessness over the other person and doing your own inner learning to discover what would be in your highest good.
I decided to deal with my anger head on. I had no idea what I was getting into, and I learned some valuable lessons along the way. These were key for me understanding that it's OK to be mad or have someone be mad at me. There is, in fact, a healthy way to deal with anger. And once I took these lessons on as truth for myself, my journey became much easier.