We aim to determine the intrinsic variety, at a given mass, of the properties of the intracluster medium in clusters of galaxies. This requires a cluster sample selected independently of the intracluster medium content for which reliable masses and subsequent X-ray data can be obtained. We present one such sample, consisting of 34 galaxy clusters selected independently of their X-ray properties in the nearby (0.050 < z < 0.135) Universe and mostly with 14 < log M₅₀₀/M_⊙ ≲ 14.5, where masses are dynamically estimated. We collected the available X-ray observations from the archives and then observed the remaining clusters with the low-background Swift X-ray telescope, which is extremely useful for sampling a cluster population expected to have low surface brightness. We found that clusters display a large range (up to a factor 50) in X-ray luminosities within r₅₀₀ at a given mass, whether or not the central emission (r < 0.15 r₅₀₀) is excised, unveiling a wider cluster population than seen in Sunayev-Zeldovich surveys or inferred from the population seen in X-ray surveys. The measured dispersion is 0.5 dex in L_X at a given mass.