Java HashSet remove item by its hash code [duplicate]

I have a class with its own hashCode() method. I am adding this class to a HashSet. How can I remove an item by its hashCode, without knowing the object itself?

For example, if I have the following code

HashSet<Data> set = new HashSet<>();
set.add(new Data(10, 5));
...
class Data {
    public int importantVal;
    public int notImportantVal;
    //... constructor ...
    @Override
    public int hashCode() {
        return importantVal;
    }
}

and I knew the importantVal of a Data object, but not the object itself. How would I remove it? set.remove(10) does not work.

Best solution I can think of is to also override equals() to return if importantVal is the same, and then do set.remove(new Data(10, anyPlaceholderValue))