Partner is either a very bad player or a good player who expects us to look deeply into the hand. Our possession of these minor high cards makes me think the former.
The main problem to solve is why he make that 6
♠ bid in an auction in which, as an unlimited hand, we took control.
I am going to infer that, since I assume he is not a good player, he fears that showing me his void via 6
♥ could be seen as natural. So I am going to guess that he has something like AKQxxxx void KQx AKx and I am going to bid 7
♠. Sure, if I am right, 7N is at least as good, but I don't have the confidence that my analysis suggests

And if he has a club void, 7
♠ may still come home while 7N, at best, needs a lucky lead.
However this turns out, I am later going to suggest to partner that when an unlimited hand takes control, the other hand stays in the boat and doesn't try to wrestle control back.
'one of the great markers of the advance of human kindness is the howls you will hear from the Men of God' Johann Hari
rduran1216 asked "Agree with the calls so far? Do you pass, correct to 6nt, or bid on at all?"
IMO 7♠ = 10, 7N = 7, Pass = 6, 6N = 5. In spite of likely bad breaks, partner was scared that you might pass his RKC response. Or perhaps he wanted to avoid a "hesitation Blackwood" auction. Hence he is likely to have super-solid trumps and possibly a void somewhere. Partner is too good for Namyats, so has 9+ tricks. I have 3 top tricks and fewer than 6 losers. IMO, failing to bid the grand would be a no-confidence vote.