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We investigate the collective behavior of a globalized society under the influence of endogenous mass media trends. The mass media trend is a global field corresponding to the statistical mode of the states of the agents in the system. The interaction dynamics is based on Axelrod's rules for the dissemination of culture. We find situations where the largest minority group, possessing a cultural state different from that of the predominant trend transmitted by the mass media, can grow to almost half of the size of the population. We show that this phenomenon occurs when a critical number of long-range connections are present in the underlying network of interactions. We have numerically characterized four phases on the space of parameters of the system: an ordered phase; a semi-ordered phase where almost half of the population consists of the largest minority in a state different from that of the mass media; a disordered phase; and a chimera-like phase where one large domain coexists with many very small domains., Competing Interests: M.G.C. work was supported by Corporación Ecuatoriana para el Desarrollo de la Investigación y Academia (CEDIA) through project CEPRA-XIII-2019 “Sistemas Complejos”, and Advanced Programming Solutions SL (APSL) provided support in the form of salary for author J.C.G.A. There are no patents or marketed products associated with this study to declare. This commercial affiliation does not alter our adherence to PLOS ONE policies on sharing data and materials.