Dependent on where the H2O is introduced into the engine and there are two options. 1) coolant spray into the compressor inlet - typical for a turboprop, as it evaporates the water cools the incoming air (latent heat of vaporisation etc etc) and increases its density.
Or 2) into the combustion chamber - more usual for axial flow turbo-jet engines!.... Thus mass flow through the turbine is increased in relation to the compressor and the turbine inlet temperature (TiT) is reduced allowing the fuel system to schedule an increased fuel flow. Vis more thrust because of a variety of effects, not least of which jet pipe pressure.
If methanol is in the mixture; that has a calorific value, as the alcohol CH3OH burns it plays the same role in the combustion chamber as the kerosene i.e. fuel!. But this does increase the TiT. Hope you keeping abreast of these explanations.