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We study the mass distribution and kinematics of the giant elliptical galaxy M87 (NGC 4486) using discrete chemo-dynamical, axisymmetric Jeans equation modelling. Our catalogue comprises 894 globular clusters (GCs) extending to a projected radius of $\sim 430$ kpc with line-of-sight velocities and colours, and Multi Unit Spectroscopic Explorer (MUSE) integral field unit data within the central $2.4$ kpc of the main galaxy. The gravitational potential for our models is a combination of a luminous matter potential with a varying mass-to-light ratio for the main galaxy, a supermassive black hole and a dark matter (DM) potential with a cusped or cored DM halo. The best-fitting models with either a cusped or a cored DM halo show no significant differences and both are acceptable. We obtain a total mass of $(2.16 \pm 0.38) \times 10^{13} M_{\odot}$ within $\sim$ 400 kpc. By including the stellar mass-to-light ratio gradient, the DM fraction increases from $\sim$ 26 percent (with no gradient) to $\sim$ 73 percent within $1\,R_e^{\rm maj}$ (major axis of half-light isophote, 14.2 kpc), and from $\sim$ 84 percent to $\sim$ 94 percent within $5\,R_e^{\rm maj}$ (71.2 kpc). Red GCs have moderate rotation with $V_{\rm max}/σ\sim$ 0.4, and blue GCs have weak rotation with $V_{\rm max}/σ\sim$ 0.1. Red GCs have tangential velocity dispersion anisotropy, while blue GCs are consistent with being nearly isotropic. Our results suggest that red GCs are more likely to be born in-situ, while blue GCs are more likely to be accreted.