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 Letter, for the first time, we employ X-ray observations to test these formation scenarios on a sample of isolated, low-surface-brightness galaxies (LSBGs). Because 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 LSBGs 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 for an average isolated LSBG. This upper limit is about 40 times lower than that expected in a galaxy with massive dark-matter halo, implying that the majority of isolated LSBGs reside in dwarf-size dark-matter halos.