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Default Maximum number of cells for 'SUM' ?

I have a spreadsheet with 56,314 rows of text labels.

I have a formula in each row off to the right of each text label. The
formula tests for a specific text string contained in the label and records a
1 if true.

At the top of the sheet above this column of formulas, I want to sum the
number of 'TRUE' responses, or 1(s).

My formula is: =SUM(I5:I56,314). But this returns a #NAME? error
message. If I limit the SUM formula to not cover beyond cell I9168, then I
get a correct answer and no error msg.

Is this a limit of Excel's ability to calculate, a limitation imposed by my
RAM resources, or something else ?
 
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