  Using Exceptional Field Theory, we determine the infinite-dimensional mass
matrices for the gravitino and spin-$1/2$ Kaluza-Klein perturbations above a
class of anti-de Sitter solutions of M-theory and massive type IIA string
theory with topologically-spherical internal spaces. We then use these mass
matrices to compute the spectrum of Kaluza-Klein fermions about some solutions
in this class with internal symmetry groups containing SU(3). Combining these
results with previously known bosonic sectors of the spectra, we give the
complete spectrum about some ${\cal N}=1$ and some non-supersymmetric solutions
in this class. The complete spectra are shown to enjoy certain generic
features.
