D H explained my post very well. There are however two exceptions:
1) Physical constants are not mentioned; for example energy and mass have very different units (kg m^2 / s^2 and kg, respectively) although multiplying by the speed of light squared converts one into the other
2) There is some specific system which makes a conversion possible, for example: a water heater doing so-many kW of work will heat so many water by 1 degree (actually, this case looks a lot like 1, with the "missing" quantity being the specific heat of water which can convert Joules to degrees per kilogram, for example).