  We probe the dynamical mass profiles of 10 galaxy clusters from the HIghest
X-ray FLUx Galaxy Cluster Sample (HIFLUGCS) using galaxy kinematics. We
numerically solve the spherical Jeans equation, and parameterize the dynamical
mass profile and the galaxy velocity anisotropy profile using two general
functions to ensure that our results are not biased towards any specific model.
The mass-velocity anisotropy degeneracy is ameliorated by using two "virial
shape parameters" that depend on the fourth moment of velocity distribution.
The resulting velocity anisotropy estimates consistently show a nearly
isotropic distribution in the inner regions, with an increasing radial
anisotropy towards large radii. We compare our derived dynamical masses with
those calculated from X-ray gas data assuming hydrostatic equilibrium, finding
that massive and rich relaxed clusters generally present consistent mass
measurements, while unrelaxed or low-richness clusters have systematically
larger total mass than hydrostatic mass by an average of 50\%. This might help
alleviate current tensions in the measurement of $\sigma_8$, but it also leads
to cluster baryon fractions below the cosmic value. Finally, our approach
probes accelerations as low as $10^{-11}$ m s$^{-2}$, comparable to the
outskirts of individual late-type galaxies. We confirm that galaxy clusters
deviate from the radial acceleration relation defined by galaxies.
