The ~800 optically unseen (R>25.5) 24mum-selected sources in the complete Spitzer First Look Survey sample (Fadda et al. 2006) with F[24mum]>0.35 mJy are found to be very strongly clustered. If, as indicated by several lines of circumstantial evidence, they are ultraluminous far-IR galaxies at z ~ [1.6-2.7], the amplitude of their spatial correlation function is very high. The associated comoving clustering length is estimated to be r_0=14.0_{-2.4}^{+2.1} Mpc, value which puts these sources amongst the most strongly clustered populations of our known universe. Their 8mum-24mum colours suggest that the AGN contribution dominates above F[24mum] ~ 0.8 mJy, consistent with earlier analyses. The properties of these objects (number counts, redshift distribution, clustering amplitude) are fully consistent with those of proto-spheroidal galaxies in the process of forming most of their stars and of growing their active nucleus, as described by the Granato et al. (2004) model. In particular, the inferred space density of such galaxies at z ~ 2 is much higher than what expected from most semi-analytic models. Matches of the observed projected correlation function w(\theta) with models derived within the so-called Halo Occupation Scenario show that these sources have to be hosted by haloes more massive than ~10^{13.4} M_⊙. This value is significantly higher than that for the typical galactic haloes hosting massive elliptical galaxies, suggesting a duration of the starburst phase of massive high-redshift dusty galaxies of T_B ~ 0.5 Gyr. ; Comment: 14 pages, 10 figures, minor revisions, to appear on MNRAS