Sum Slopes at infinity

Calculus Level pending

The function \({ x }^{ 3 }+{ y }^{ 3 }=1\) has a slope of m as x approaches negative infinity, and a slope of n as y approaches negative infinity.

If:

\(\displaystyle \sum _{ i=0 }^{ \infty }{ { m }^{ i } } +\sum _{ j=2 }^{ \infty }{ { n }^{ j } } = q\) ;

Then what is the largest value that q can have?

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