We apply the relativistic precession (RP) model with its variants and the resonance epicyclic model with its variants, based on the frequencies of the geodesic epicyclic motion in the field of a Kerr black hole, to put limits on the mass of the black hole in the ultraluminous X-ray source M82 X-1 demonstrating twin high-frequency quasi-periodic oscillations (HF QPOs) with the frequency ratio near 3:2. The mass limits implied by the geodesic HF QPO models are compared to those obtained due to the model of string loop oscillations around a stable equilibrium position. Assuming the whole range of the black hole dimensionless spin, 0 < a < 1, the restrictions on the black hole mass related to the twin HF QPOs are widely extended and strongly model dependent; nevertheless, they give the lower limit M_{M82 (X-1)} > 130 M_{circle dot} confirming existence of an intermediate black hole in the M82 X-1 source. The upper limit given by one of the variants of the geodesic twin HF QPO models goes u