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We present the results of a direct detection search for mirror dark matter interactions, using data collected from the Large Underground Xenon experiment during 2013, with an exposure of 95 live-days × 118 kg. Here, the calculations of the mirror electron scattering rate in liquid xenon take into account the shielding effects from mirror dark matter captured within the Earth. Annual and diurnal modulation of the dark matter flux and atomic shell effects in xenon are also accounted for. Having found no evidence for an electron recoil signal induced by mirror dark matter interactions we place an upper limit on the kinetic mixing parameter over a range of local mirror electron temperatures between 0.1 and 0.9 keV. This limit shows significant improvement over the previous experimental constraint from orthopositronium decays and significantly reduces the allowed parameter space for the model. We exclude mirror electron temperatures above 0.3 keV at a 90% confidence level, for this model, and constrain the kinetic mixing below this temperature.