Reporting back a cell value using SUMIF (multiple sheets)

Ok, I'm going to try this again. Say I have the following information in my spreadsheet:

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My spreadsheet tracks various information throughout the month (each day is on it's own sheet). The last sheet is a summary page with various totals and averages. There is also a calculation that figures the max duration for the month: ex. =MAX('11-01:11-30'!a2:a4). Now, I would like to also report the date that is located in a10 next to that max value. That way, the users of the sheet can easily be pointed to the date of the unusually long duration. This example is a simplified demonstration of the actual sheet, but should suffice. I tried using SUMIF, but that doesn't seem to work. I tried using the following: =SUMIF('11-01:11-30'!a2:a4,"=max('11-01:11-30'!a2:a4)",'11-01:11-30'!a10). Any suggestions?

Thanks much,
Kris