Let $f(x) = ax + b,$ where $a$ and $b$ are constants.  If $f(f(f(x))) = 8x + 21,$ find $a + b.$
<|im_start|>system
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<|im_start|>user
Let $f(x) = ax + b,$ where $a$ and $b$ are constants.  If $f(f(f(x))) = 8x + 21,$ find $a + b.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
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user
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Let $f(x) = ax + b,$ where $a$ and $b$ are constants.  If $f(f(f(x))) = 8x + 21,$ find $a + b.$
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