The extra dimensions posited by m-theory are curled-up into something known as a Calabi-Yau manifold which exists at every point in spacetime (notice that we are straight away assuming that the GR model of 'smooth' spacetime is wrong - something which we are pretty sure of - it almost certainly must quantise).
It isn't metaphysics for the simple reason that it is testable - we just haven't had either the mathematics to make detailed predictions or the kit to poke away at the problem and give the theoreticians something to work with.
One prediction would be that gravity will not obey the inverse-square law at the smallest scales. As you get down to the Planck length then gravity is going to change. One possible outcome is the much talked-about formation of Micro-black holes. QED tells us that no such thing is possible if we use GMm/r^2 for the calculations. If MBH are observed at LHC then it would be strong circumstantial evidence for multiple dimensions.
More reading
http://www.slac.stanford.edu/...f/C9808031/pdf/ssi98-008.pdf
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