Sum of Reciprocals

Algebra Level 5

\(9\) distinct positive integers are given, such that the sum of their reciprocals is equal to \(1\). If \(5\) of these integers are \(3, 7, 9, 11\) and \(33\), and the other \(4\) integers all have a units digit of \(5\), what is the sum of these \(9\) integers?

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