Recent advancements in the imaging of low-surface-brightness objects revealed numerous ultra-diffuse galaxies in the local Universe. These peculiar objects are unusually extended and faint: their effective radii are comparable to the Milky Way, but their surface brightnesses are lower than that of dwarf galaxies. Their ambiguous properties motivate two potential formation scenarios: the failed Milky Way and the dwarf galaxy scenario. In this paper, for the first time, we employ X-ray observations to test these formation scenarios on a sample of isolated, low-surface-brightness galaxies. Since hot gas X-ray luminosities correlate with the dark matter halo mass, failed Milky Way-type galaxies, which reside in massive dark matter halos, are expected to have significantly higher X-ray luminosities than dwarf galaxies, which reside in low-mass dark matter halos. We perform X-ray photometry on a subset of low-surface-brightness galaxies identified in the Hyper Suprime-Cam Subaru survey, utilizing the XMM-Newton XXL North survey. We find that none of the individual galaxies show significant X-ray emission. By co-adding the signal of individual galaxies, the stacked galaxies remain undetected and we set an X-ray luminosity upper limit of ${L_{rm{0.3-1.2keV}}leq6.2 times 10^{37} (d/65 rm{Mpc})^2 rm{erg s^{-1}}}$ for an average isolated low-surface-brightness galaxy. This upper limit is about 40 times lower than that expected in a galaxy with a massive dark matter halo, implying that the majority of isolated low-surface-brightness galaxies reside in dwarf-size dark matter halos.
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