To solve $ \dfrac1m+\dfrac1n-\dfrac1{mn^2}=\dfrac34$ on all integers

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Refering To solve $ \dfrac1m+\dfrac1n-\dfrac1{mn^2}=\dfrac34$ , I think it is an interesting question, if the possible solution are integers, thus

How do we find all integers $(m,n)$ such that $ \dfrac1m+\dfrac1n-\dfrac1{mn^2}=\dfrac34$?