A different type of algebra problem 2

Algebra Level 5

\[ \large \displaystyle\sum _{ n=1 }^{ 5 }{ { x }^{ { n }^{ 2 } } } =\displaystyle\sum _{ n=1 }^{ 4 }{ { x }^{ { (-n) }^{ n } } } \]

How many real solutions does the above equation have?

Enter 1729 if you think that there are an infinite number of solutions

Bonus: Find all these solutions.

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