An \(N\)-sided die

Jorge has an \(N\)-sided fair die and wonders how many times he would need to roll it until he has rolled all the numbers from \(1\) to \(N\) (in any order).

He does a quick calculation and discovers that the expected value for the number of rolls is 91 when rounding to the nearest integer.

How many sides does his die have?

Clarification: One distinct number from \(1\) to \(N\) is printed on each face of the die.

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