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We probed the dynamical mass profiles of ten galaxy clusters from the HIghest X-ray FLUx Galaxy Cluster Sample (HIFLUGCS) using galaxy kinematics. We numerically solved 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 toward 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 toward large radii. We compared 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 masses than hydrostatic masses by, on average, 50%. This might help alleviate current tensions in the measurement of σ8, 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. [ABSTRACT FROM AUTHOR]