High-energy radiotherapy treatments of a medical Linear Accelerator (LinAc) generate secondary neutrons that can produce health damage on the human body as the induction of secondary cancers. The energy spectrum of these neutrons must be determined to estimate the extra dose received by patients inside a radiotherapy room during radiotherapy treatment. To quantify the neutron production, a Ludlum Bonner sphere spectrometer (BSS) is used for measurement at different points of a LinAc bunker at the Hospital Universitari i Politècnic La Fe de València. With the neutron measured data and a set of response detector curves obtained by Monte Carlo simulations with MCNP6.1.1, the Maximum Likelihood Expectation Maximization unfolding method is used to unfold the energy neutron spectrum. Unfolded neutron spectra at different locations were compared to those obtained by Monte Carlo simulation of the same setup, showing the same energetic behavior. The fluence rate decreases with source distance, and the shape changes from a fast neutron peak in the nearest LinAc head location to a prominent thermal neutron peak in the bunker maze region. Moreover, the neutron ambient equivalent dose was obtained from the unfolded spectra and compared to Berthold detector measurements, being consistent.