One of the most fundamental questions in galaxy evolution is how galaxies regulate nuclear growth and accretion onto supermassive black holes. One potential way to do this is through a galactic wind which removes gas from the nucleus. It is unclear whether galactic winds are powered by jets, mechanical winds, radiation, or via magnetohydrodynamic processes. Compact obscured nuclei (CONs) represent a significant phase of galactic nuclear growth. These galaxies hide growing supermassive black holes or unusual starbursts in their very opaque, extremely compact (r < 100 pc) centres. They are found in approximately 30% of the luminous and ultra-luminous infrared galaxy (LIRG and ULIRG) population. Here, we present high resolution ALMA observations (~30mas, ~5pc) of ground-state and vibrationally excited HCN towards ESO 320-G030 (IRAS 11506−3851). ESO 320-G030 is an isolated luminous infrared galaxy known to host a compact obscured nucleus and a kiloparsec-scale molecular wind. Our analysis of these high-resolution observations excludes the possibility of a starburst driven wind, a mechanically or energy driven AGN wind, and exposes a molecular magnetohydrodynamic wind. If magnetohydrodynamic winds are intrinsic to CONs, these results imply that nuclear evolution of galaxies and growth of SMBHs is similar to the growth of hot cores or protostars, and that star formation or active galactic nuclei feedback may not be necessary to drive galactic winds.