Tricky Algebra! (Are 1 & -1 somehow related?)

Algebra Level 5

$\large f\left( x \right) ={ x }^{ 6 }+a{ x }^{ 5 }+b{ x }^{ 4 }{ +x }^{ 3 }{ +bx }^{ 2 }+a{ x }^{ 1 }+1{ x }^{ 0 }$ If 1 is a root of $$f(x)$$ while -1 is not, then what is the maximum number of distinct real roots that $$f(x)$$ can have?

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