We study the relation between stellar mass (M-*) and star formation rate (SFR) for star-forming galaxies over approximately five decades in stellar mass (5.5 less than or similar to log(10)(M-*/M-circle dot) less than or similar to 10.5) at z approximate to 3-6.5. This unprecedented coverage has been possible thanks to the joint analysis of blank non-lensed fields (COSMOS /SMUVS) and cluster lensing fields (Hubble Frontier Fields) that allow us to reach very low stellar masses. Previous works have revealed the existence of a clear bimodality in the SFR-M-* plane with a star formation Main Sequence and a starburst cloud at z approximate to 4-5. Here we show that this bimodality extends to all star-forming galaxies and is valid in the whole redshift range z approximate to 3-6.5. We find that starbursts constitute at least approximate to 20% of all star-forming galaxies with M-* greater than or similar to 10(9) M-circle dot at these redshifts and reach a peak of 40% at z = 4-5. More importantly, 60%-90% of the total SFR budget at these redshifts is contained in starburst galaxies, indicating that the starburst mode of star formation is dominant at high redshifts. Almost all the low stellar mass starbursts with log(10)(M-*/M-circle dot) less than or similar to 8.5 have ages comparable to the typical timescales of a starburst event, suggesting that these galaxies are being caught in the process of formation. Interestingly, galaxy formation models fail to predict the starburst/main-sequence bimodality and starbursts overall, suggesting that the starburst phenomenon may be driven by physical processes occurring at smaller scales than those probed by these models.