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

$\large f\left( x \right) ={ x }^{ 6 }+a{ x }^{ 5 }+b{ x }^{ 4 }{ +x }^{ 3 }{ +bx }^{ 2 }+a{ x }^{ 1 }+1{ x }^{ 0 }$ 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?