  We have discovered that SDSSJ105213.51+442255.7 (T0.5$\pm$1.0) is a binary in
Keck laser guide star adaptive optics imaging, displaying a large J-to-K-band
flux reversal ($\Delta$J = -0.45$\pm$0.09 mag, $\Delta$K = 0.52$\pm$0.05 mag).
We determine a total dynamical mass from Keck orbital monitoring (88$\pm$5
$M_{\rm Jup}$) and a mass ratio by measuring the photocenter orbit from
CFHT/WIRCam absolute astrometry ($M_B/M_A$ = 0.78$\pm$0.07). Combining these
provides the first individual dynamical masses for any field L or T dwarfs,
49$\pm$3 $M_{\rm Jup}$ for the L6.5$\pm$1.5 primary and 39$\pm$3 $M_{\rm Jup}$
for the T1.5$\pm$1.0 secondary. Such a low mass ratio for a nearly equal
luminosity binary implies a shallow mass$-$luminosity relation over the L/T
transition ($\Delta$log$L_{\rm bol}$/$\Delta$log$M = 0.6^{+0.6}_{-0.8}$). This
provides the first observational support that cloud dispersal plays a
significant role in the luminosity evolution of substellar objects. Fully
cloudy models fail our coevality test for this binary, giving ages for the two
components that disagree by 0.2 dex (2.0$\sigma$). In contrast, our observed
masses and luminosities can be reproduced at a single age by "hybrid"
evolutionary tracks where a smooth change from a cloudy to cloudless
photosphere around 1300 K causes slowing of luminosity evolution. Remarkably,
such models also match our observed JHK flux ratios and colors well. Overall,
it seems that the distinguishing features SDSSJ1052+4422AB, like a J-band flux
reversal and high-amplitude variability, are normal for a field L/T binary
caught during the process of cloud dispersal, given that the age
(1.11$^{+0.17}_{-0.20}$ Gyr) and surface gravity (log$g$ = 5.0$-$5.2) of
SDSSJ1052+4422AB are typical for field ultracool dwarfs.
