The specific chemistry of added salt has a strong effect on the aggregation of surfactants. Although the molecular mechanism of this effect is still debated in the literature and there is no generally accepted quantitative theory, substantial progress has recently been achieved in the molecular thermodynamic modeling of ion-specific effects for solutions of ionic surfactants. In this work, we extend our previous aggregation model of ionic surfactants to solutions of nonionic surfactants in the presence of salts. Within this model, the specificity of ions is reflected by the difference in ionic diameters, the dispersion interaction with the micelle, and an effective parameter δ_± that takes into account the hydration/dehydration of an ion in the micellar corona and is specific to every ion-surfactant head pair. The effect of specific salt on the hydrophobic contribution to the aggregation free energy is described via the Setchenov salting-out constants. We apply the model for sugar-based surfactants: n-alkyl glucosides and N-acyl-N-methylglucosides. This choice is motivated by the importance of this family of surfactants in biotechnology. We report the set of model parameters, including the Setchenov constants, for the surfactants in this family in combination with a number of 1:1 salts and illustrate good performance of the model in the description of the specific effect of added salt on the critical micelle concentration (CMC) and the growth of micellar aggregates.