  We use exceptional field theory to describe locally non-geometric spaces of
M-theory of more than three dimensions. For these spaces, we find a new set of
locally non-geometric fluxes which lie in the R-R sector in the weak-coupling
limit and can typically be characterised by mixed symmetry tensors. These
spaces thus provide new examples of non-geometric backgrounds which go beyond
the NS-NS sector of string theory. Starting from twisted tori we construct
duality chains that lead to these new non-geometric backgrounds and we show
that, just as in the four-dimensional case, there are missing momenta
associated to the mixed symmetry tensors.
