Can I extend incoming 5ghz on 2.4ghz? (n600 or ac750)

I am interested in a range extender which extends a 5GHz signal on both 2.4GHz and 5GHz.

My cable modem/wireless router has a weak 2.4GHz signal, not reliably seeable where I want to put the range extender. 5GHz is just fine. (I've checked with software that shows me all the wireless access points and their signal strengths.)

So can I connect the extender to the 5GHz, and have it repeat as an access point on both 5 and 2.4?

I think the problem this is due to interference from several neighbors, but no matter. Changing the 2.4Ghz channel between 1, 6, 11 doesn't fix the problem.

I am looking at both the EX6100 and WN2500rp, they are available and in my price range.

(I borrowed a small Belkin extender to see how this all works, and it *doesn't* do this. So I figured I would ask before buying. My searching the support forums didn't pull up an answer, possibly because I don't have a good handle on specific search terms.)