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If $x + \frac{1}{x} = 1$, then find the value of

$x+{ x }^{ 4 }+{ x }^{ 7 }+{ x }^{ 10 }+{ x }^{ 19 }+{ x }^{ 22 }+{ x }^{ 25 }+{ x }^{ 31 }+{ x }^{ 34 }+{ x }^{ 40 }.$

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