Does this card let me resolve BOTH melee and ranged dice since its says either or?

Resolve *one* of your dice - So while you can resolve dice with either kind of damage, it will only let you resolve one dice.

But the card reads "Resolve one or more of your dice..."

Wow, sorry. Shows what I get for assuming, rather than actually reading the card. I'd thought it was just one dice, like most effects.

I'd say no. 'Either' in this case I think means you have to pick one; otherwise it could have just been 'Resolve one or more of your dice showing melee or ranged damage', and would have had the same effect.

I agree with Abyss. Compare this wording with that used on the Secret Facility - Scarif battlefield - 'Resolve up to 3 of your dice showing damage'.

One thing to consider

If you have an enemy on 2 damage and one on full health for one action you could resolve say 3 melee dice  dealing 2 damage to one, 2 damage to another and the loose a resource 

It's not an amazing card but versatile and basically adds a kicker to some damage and gives you some options on how to resolve multiple dice as action efficiency