Although it is often repeated, there is no rule where we sum the locants. We use the set of locants that has the lowest number at the first point of difference when arranged in increasing order. This will not necessarily give us the same answer as the lowest sum.
For your molecule (ignoring the 1,4-diene bit as it's the same in both names) the sets of locants are:
3,6,6
3,3,6
The first point of difference is the second number in each set, 3 is lower than 6, so the bottom name is correct.