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Note that utilitarianism need not be based only on hedonism, that is, seeking pleasure and avoiding pain.
Imagine that someone considers diverse things good; pleasure might be one of these things, and absence of pain might be another, but there might be others.
Furthermore, imagine that how much the person likes some of these things depends on how much they have, and also upon the status of the others, and also upon the status of other people; for example, maybe someone would like food very much when they have little, but would not care for it when they have a lot of food already; or imagine that someone greatly desires money if others around them have a lot more of it than they, but would rather have other good things if others around them have little; or imagine that someone's desire for comfort and luxury is little when they feel in danger, but greater when they feel safe.
These can all be handled simply by making 'utility' the output of a function whose inputs are the state of the diverse potential goods that the person cares about (including the good of 'equality' or 'fairness'). Like a 'joint probability distribution, there is no need for this 'joint individual utility' function to just assign a value to each unit of each good and then sum them separately; the total utility can depend on interactions between the amounts of the goods.
