If you cannot claim territory or occupy it, how do you acquire the legal right to mine in the first place?
In any case this was litigated many decades ago (pre-internet) and the upshot is mining can only be done if all parties agree and all parties benefit. It was so long ago, I do not remember who what or where - you will have to find that info on your own.
No differently than fishing in international waters.
It appears the US government doesn't agree with you.