The observational study of star formation laws is paramount to disentangling the physical processes at work on local and global scales in galaxies. To this aim we have expanded the sample of extreme starbursts, represented by local LIRGs and ULIRGs, with high-quality data obtained in the 1-0 line of HCN. The analysis of the new data shows that the star formation efficiency of the dense molecular gas, derived from the FIR/HCN luminosity ratio, is a factor 3-4 higher in extreme starbursts compared to normal galaxies. We find a duality in the Kennicutt-Schmidt laws that is enhanced if we account for the different conversion factor for HCN (αHCN) in extreme starbursts and correct for the unobscured star formation rate in normal galaxies. We find that it is possible to fit the observed differences in the FIR/HCN ratios between normal galaxies and LIRGs/ULIRGs with a common constant star formation rate per free-fall time (SFRff) if we assume that HCN densities are ∼1–2 orders of magnitude higher in LIRGs/ULIRGs, and provided that SFRff∼0.005-0.01 and/or if αHCN is a factor of a few lower than our favored values.