I have at best a rudimentary understanding of the math in this side of physics, so bear with me. I am also aware of this question, but it was asked and answered 4 years ago and I don't want to gravedig.
I've gone with 10 spatial dimensions, as that's what M-Theory requires, but this question would be the same with 9 spatial dimensions (as regular String Theory has).
That question's answer assumes other dimensions are external (albeit alongside) our universe. Do we know that for a fact? Surely, just as you could take a 1- or 2-dimensional slice through our universe and call it a dimension, is our universe but a 3-dimensional slice through an actually 10-dimensional space? This is completely different from the view of having the extra dimensions folded up in a "Calabi-Yau manifold" somewhere, which, while convenient for the math, seems unlikely. (Why would the universe have 3 nicely open dimensions, and 7 more folded into some obscure mathematical shape? It flies in the face of physics solutions being graceful and neat...)
Having our observable dimensions be a slice through a 10-dimensional space would mean there can be matter distributed evenly throughout the entire 10 dimensions, very close to the 3 dimensions we can see but not actually residing in them. (And surely if there are 7 more dimensions, they wouldn't be empty and just sitting there, they would have matter in them!)
Finally, the main question. The matter in these dimensions should definitely have a gravitational effect on the matter in our observable dimensions. Could this gravitational effect be the same effect that we currently categorize as being due to 'dark matter' or 'dark energy', and thus, is it actually possible that the 'dark matter' we know exists is actually regular matter, residing in another dimension?
EDIT: I removed the dubious math and conjectures, cause that made it seem more like a personal theory (it's now more clear now that this is about one specific question rather than "confirm theory pls")