We present X-ray , optical , near-infrared ( IR ) , and radio observations of GRBs 110709B and 111215A , as well as optical and near-IR observations of their host galaxies . The combination of X-ray detections and deep optical/near-IR limits establish both bursts as ‘ ‘ dark ’ ’ . Sub-arcsecond positions enabled by radio detections lead to robust host galaxy associations , with optical detections that indicate z \lesssim 4 ( 110709B ) and z \approx 1.8 - 2.7 ( 111215A ) . We therefore conclude that both bursts are dark due to substantial rest-frame extinction . Using the radio and X-ray data for each burst we find that GRB 110709B requires A _ { V } ^ { host } \gtrsim 5.3 mag and GRB 111215A requires A _ { V } ^ { host } \gtrsim 8.5 mag ( z = 2 ) . These are among the largest extinction values inferred for dark bursts to date . The two bursts also exhibit large neutral hydrogen column densities of N _ { H,int } \gtrsim 10 ^ { 22 } cm ^ { -2 } ( z = 2 ) as inferred from their X-ray spectra , in agreement with the trend for dark GRBs . Moreover , the inferred values are in agreement with the Galactic A _ { V } - N _ { H } relation , unlike the bulk of the GRB population . Finally , we find that for both bursts the afterglow emission is best explained by a collimated outflow with a total beaming-corrected energy of E _ { \gamma } + E _ { K } \approx ( 7 - 9 ) \times 10 ^ { 51 } erg ( z = 2 ) expanding into a wind medium with a high density , \dot { M } \approx ( 6 - 20 ) \times 10 ^ { -5 } M _ { \odot } yr ^ { -1 } ( n \approx 100 - 350 cm ^ { -3 } at \approx 10 ^ { 17 } cm ) . While the energy release is typical of long GRBs , the inferred density may be indicative of larger mass loss rates for GRB progenitors in dusty ( and hence metal rich ) environments . This study establishes the critical role of radio observations in demonstrating the origin and properties of dark GRBs . Observations with the JVLA and ALMA will provide a sample with sub-arcsecond positions and robust host associations that will help to shed light on obscured star formation and the role of metallicity in GRB progenitors .