Divisibility Of Power Differences

Number Theory Level 4

Let $a$ and $b$ be positive integers with $a>b$ such that $7!\Big|\big(x^a-x^b\big)$ for all integers $x.$

Find the smallest possible value of $a+b.$

Clarification: $!$ denotes the factorial notation. For example, $8! = 1\times2\times3\times\cdots\times8$ .

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