We present individual dynamical masses for the nearby M9.5+T5.5 binary WISE J072003.20$-$084651.2AB, a.k.a. Scholzs star. Combining high-precision CFHT/WIRCam photocenter astrometry and Keck adaptive optics resolved imaging, we measure the first high-quality parallactic distance ($6.80_{-0.06}^{+0.05}$ pc) and orbit ($8.06_{-0.25}^{+0.24}$ yr period) for this system composed of a low-mass star and brown dwarf. We find a moderately eccentric orbit ($e = 0.240_{-0.010}^{+0.009}$), incompatible with previous work based on less data, and dynamical masses of $99pm6$ $M_{rm Jup}$ and $66pm4$ $M_{rm Jup}$ for the two components. The primary mass is marginally inconsistent (2.1$sigma$) with the empirical mass$-$magnitude$-$metallicity relation and models of main-sequence stars. The relatively high mass of the cold ($T_{rm eff} = 1250pm40$ K) brown dwarf companion indicates an age older than a few Gyr, in accord with age estimates for the primary star, and is consistent with our recent estimate of $approx$70 $M_{rm Jup}$ for the stellar/substellar boundary among the field population. Our improved parallax and proper motion, as well as an orbit-corrected system velocity, improve the accuracy of the systems close encounter with the solar system by an order of magnitude. WISE J0720$-$0846AB passed within $68.7pm2.0$ kAU of the Sun $80.5pm0.7$ kyr ago, passing through the outer Oort cloud where comets can have stable orbits.
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