Can you confirm that the error you are seeing is the error value: VALUE#!
or is it a row of ######'s
SUM() is quite tolerant of non-numeric values and usually only returns #VALUE! if one of the cells in the SUM(range) has an #VALUE! error.
I am assuming that none of the individual time durations is giving an error.
As DerbyDad03's post shows, SUM() works for adding individual times, so the error is not the SUM() function itself.
Excel displays a row of #s if the date/time will not fit in the cell (widen the column), or if the result of the date/time calculation is negative.