Separable Integers Reloaded

An integer is said to be nine-separable if it can be represented as the product of two positive integers that differ by nine. (For example, since \(22=2\times 11\), \(22\) is nine-separable.) Similarly, an integer is said to be eighteen-separable if it can be represented as the product of two positive integers that differ by \(18\). What is the sum of all positive integers that are both nine-separable and eighteen-separable?

Inspiration drawn from Seperable Integers by David Altizio

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