mshafi,
You want to keep the minutes as an integer since that's what they really are (and then you can aggregate them as well.) So keep the duration as an integer and just format the display. Here's how I would handle this:
Let's call the acutal measure Duration. Now create a calculated measure called DurationFormatted. If you convert a number greater than zero to date/time, SSAS sees it as the number of days; in other words, 58 would be 58 days. Since you would have 58 as the number of minutes, you'll need to divide it by 1440 (the number of minutes in a day.) If you had hours you would divide by 24; if you had seconds you would divide by 86400.
Anyway, this is what your formula would look like:
format(cdate([Measures].Duration/1440 - int([Measures].Duration/1440)),"hh:mm:ss")
Now, I had an issue that the empty cells were no longer empty so I changed the final formula to this:
IIF([Measures].Duration=0,NULL,format(cdate([Measures].Duration/1440 - int([Measures].Duration/1440)),"hh:mm:ss"))
If you were doing this in BIDS, it would look like this figure:

Finally, when you process the cube, you can see the effect. I had two values, 58 and 123 minutes. You can see that the sum is three hours and one minute, and that the format is correct.
