The Cygnus X complex is covered by the Global View of Star Formation in the Milky Way (GLOSTAR) survey, an unbiased radio-wavelength Galactic plane survey, in 4--8 GHz continuum radiation and several spectral lines. The GLOSTAR survey observed the 6.7~GHz transition of methanol (CH$_3$OH), an exclusive tracer of high-mass young stellar objects. Using the Very Large Array in both the B and D configurations, we observed an area in Cygnus~X of $7^{rm o}times3^{rm o}$ in size and simultaneously covered the methanol line and the continuum, allowing cross-registration. We detected thirteen sources with Class~II methanol maser emission and one source with methanol absorption. Two methanol maser sources are newly detected; in addition, we found four new velocity components associated with known masers. Five masers are concentrated in the DR21 ridge and W75N. We determined the characteristics of the detected masers and investigated the association with infrared, (sub)millimeter, and radio continuum emission. All maser sources are associated with (sub)millimeter dust continuum emission, which is consistent with the picture of masers tracing regions in an active stage of star formation. On the other hand, only five masers ($38pm17%$) have radio continuum counterparts seen with GLOSTAR within $sim$1$$, testifying to their youth. Comparing the distributions of the bolometric luminosity and the luminosity-to-mass ratio of cores that host 6.7~GHz methanol masers with those of the full core population, we identified lower limits $L_{rm Bol}sim200~L_odot$ and $L_{rm Bol}/M_{rm core}sim1~L_odot~M^{-1}_odot$ for a dust source to host maser emission.
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