We perform in-depth dynamical modelling of the luminous and dark matter (DM) content of the elliptical galaxy NGC 1407. Our strategy consists of solving the spherical Jeans equations for three independent dynamical tracers: stars, blue GCs and red GCs in a self-consistent manner. We adopt a maximum-likelihood Markov-Chain Monte Carlo fitting technique in the attempt to constrain the inner slope of the DM density profile (the cusp/core problem), and the stellar initial mass function (IMF) of the galaxy. We find the inner logarithmic slope of the DM density profiles to be $gamma = 0.6pm0.4$, which is consistent with either a DM cusp ($gamma = 1$) or with a DM core $(gamma = 0)$. Our findings are consistent with a Salpeter IMF, and marginally consistent with a Kroupa IMF. We infer tangential orbits for the blue GCs, and radial anisotropy for red GCs and stars. The modelling results are consistent with the virial mass--concentration relation predicted by $Lambda$CDM simulations. The virial mass of NGC 1407 is $log$ $M_{rm vir} = 13.3 pm 0.2 M_{odot}$, whereas the stellar mass is $log M_* = 11.8 pm 0.1 M_{odot}$. The overall uncertainties on the mass of NGC 1407 are only 5 per cent at the projected stellar effective radius. We attribute the disagreement between our results and previous X-ray results to the gas not being in hydrostatic equilibrium in the central regions of the galaxy. The halo of NGC 1407 is found be DM dominated, with a dynamical mass-to-light ratio of $M/L=260_{-100} ^{+174} M_{odot}/L_{odot, B}$. However, this value can be larger up to a factor of 3 depending on the assumed prior on the DM scale radius.
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