We present optical, near-infrared, and radio observations of the afterglow of GRB 120521C. By modeling the multi-wavelength dataset, we derive a photometric redshift of z~6.0, which we confirm with a low signal-to-noise ratio spectrum of the afterglow. We find that a model with a constant-density environment provides a good fit to the afterglow data, with an inferred density of 0.05/cm^3. The radio observations reveal the presence of a jet break at 7 d, corresponding to a jet opening angle of ~ 3 deg. The beaming-corrected gamma-ray and kinetic energies are both ~ 3e50 erg. We quantify the uncertainties in our results using a detailed Markov Chain Monte Carlo analysis, which allows us to uncover degeneracies between the physical parameters of the explosion. To compare GRB 120521C to other high-redshift bursts in a uniform manner we re-fit all available afterglow data for the two other bursts at z>6 with radio detections (GRBs 050904 and 090423). We find a jet break at ~ 15 d for GRB 090423, in contrast to previous work. Based on these three events, we find that GRBs at z>6 appear to explode in constant-density environments, and exhibit a wide range of energies and densities that span the range inferred for lower redshift bursts. On the other hand, we find a hint for narrower jets in the z>6 bursts, potentially indicating a larger true event rate at these redshifts. Overall, our results indicate that long GRBs share a common progenitor population at least to z~8.
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