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Default SUM 3D Reference using variable sheet limits

I want to SUM the values in the X35 cells from multiple sheets named for
months (Nov2008 . . May2009 etc.). I need to be able to easily change the
limits of the sheets to be included in the calculation, (ie: Nov2008 . . May
2009, then recalculate for Jan2009 . . April2009).

AD31 will contain the name of the first included sheet ('Nov2008), AF31 will
contain the name of the last included sheet ('May2009).

=SUM(INDIRECT(AD31:AF31&"!X35"))
returns an incorrect number. I think it is missing the fact that the cell
references refer to sheets, not cells. What formula or modification do I
need?