We present the results of an X-ray mass analysis of the early-type galaxy NGC 4636, using Chandra data. We have compared the X-ray mass density profile with that derived from a dynamical analysis of the systems globular clusters (GCs). Given the observed interaction between the central active galactic nucleus and the X-ray emitting gas in NGC 4636, we would expect to see a discrepancy in the masses recovered by the two methods. Such a discrepancy exists within the central ~10kpc, which we interpret as the result of non-thermal pressure support or a local inflow. However, over the radial range ~10-30kpc, the mass profiles agree within the 1-sigma errors, indicating that even in this highly disturbed system, agreement can be sought at an acceptable level of significance over intermediate radii, with both methods also indicating the need for a dark matter halo. However, at radii larger than 30kpc, the X-ray mass exceeds the dynamical mass, by a factor of 4-5 at the largest disagreement. A Fully Bayesian Significance Test finds no statistical reason to reject our assumption of velocity isotropy, and an analysis of X-ray mass profiles in different directions from the galaxy centre suggests that local disturbances at large radius are not the cause of the discrepancy. We instead attribute the discrepancy to the paucity of GC kinematics at large radius, coupled with not knowing the overall state of the gas at the radius where we are reaching the group regime (>30kpc), or a combination of the two.