We report the discovery and detailed monitoring of X-ray emission associated with the Type IIb SN 2011dh using data from the Swift and Chandra satellites , placing it among the best studied X-ray supernovae to date . We further present millimeter and radio data obtained with the SMA , CARMA , and EVLA during the first three weeks after explosion . Combining these observations with early optical photometry , we show that the panchromatic dataset is well-described by non-thermal synchrotron emission ( radio/mm ) with inverse Compton scattering ( X-ray ) of a thermal population of optical photons . In this scenario , the shock partition fractions deviate from equipartition by a factor , ( \epsilon _ { e } / \epsilon _ { B } ) \sim 30 . We derive the properties of the shockwave and the circumstellar environment and find a time-averaged shock velocity of \overline { v } \approx 0.1 c and a progenitor mass loss rate of \dot { M } \approx 6 \times 10 ^ { -5 } ~ { } M _ { \odot } ~ { } yr ^ { -1 } ( for an assumed wind velocity , v _ { w } = 1000 ~ { } km~ { } s ^ { -1 } ) . We show that these properties are consistent with the sub-class of Type IIb supernovae characterized by compact progenitors ( Type cIIb ) and dissimilar from those with extended progenitors ( Type eIIb ) . Furthermore , we consider the early optical emission in the context of a cooling envelope model to estimate a progenitor radius of R _ { * } \approx 10 ^ { 11 } cm , in line with the expectations for a Type cIIb supernova . Together , these diagnostics are difficult to reconcile with the extended radius of the putative yellow supergiant progenitor star identified in archival HST observations , unless the stellar density profile is unusual . Finally , we searched for the high energy shock breakout pulse using X-ray and gamma-ray observations obtained during the purported explosion date range . Based on the compact radius of the progenitor , we estimate that the shock breakout pulse was detectable with current instruments but likely missed due to their limited temporal/spatial coverage . Future all-sky missions will regularly detect shock breakout emission from compact SN progenitors enabling prompt follow-up observations with sensitive multi-wavelength facilities .