The polynomial $x^6 + ax + b$ is divisible by $x^2 - 2x - 1.$  Find $a + b.$
<|im_start|>system
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<|im_start|>user
The polynomial $x^6 + ax + b$ is divisible by $x^2 - 2x - 1.$  Find $a + b.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
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The polynomial $x^6 + ax + b$ is divisible by $x^2 - 2x - 1.$  Find $a + b.$
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