Kant vs Mill - Preference and Universality

If you look closely at Mill’s arguments in Utilitarianism, he seems to be making a very strong response to Kant (perhaps against the Groundwork?). Mill accepts the notion of moral duty, just as Kant does. But he insists it derives not from any form of analytic (i.e., Kant’s notion of synthetic a priori) truth. Rather, Mill insists it derives from the apparently universal desire of mankind (individually, in aggregate) to seek its own pleasure.