A different type of algebra problem

Algebra Level 5

\[\large \displaystyle\sum _{ n=1 }^{ 9 }{ { x }^{ (-1)^{ n } } } =\displaystyle\sum _{ n=1 }^{ 13 }{ { x }^{ n } } \]

How many real solutions does the above equation have?

Bonus: Find them (I don't think they have a nice closed form at all).

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