You have 7 nut outs (Ah, 3 non-heart Js and 3 non-heart 6s) that you could hit on the turn. The call in front of you after the initial bet likely means that some of your outs are dead. Your initial pot sized raise isn't terrible as you stand a chance to pick up the pot with it and/or force out the nut-flush draw.

The fact that you were min-raised should raise an eyebrow, IMO. If this was a good player, it probably means a better wrap and flush draw or a set w/ nut flush or straight draw.

There really isn't a reasonable hand that your opponent could hold that you are better than a coin flip against. There are quite a few hands where you are a signigicant dog though. So, given that, I would probably elect to simply call his min raise and see what the turn brings.