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I think you're highly likely the best hand on the flop, and should lead rather than giving free cards. I'd expect an underpair to raise you here to find out if you're serious and you need to come back over the top. If they smooth call on the flop, my danger sense is going off. The turn blank would likely be enough to encourage me to put in another bet, probably T80-T90. (You don't want people drawing on straights to get odds to suck out here, but you also don't want to completely commit)

In your hand, I think I call the minraise and check, but I think I'd fold the river without a read if I don't improve.