# Mr. 11 is back to the game!

If $$x,y,z \in \mathbb{Z},$$ $$-100 \leq x,y,z \leq 100$$ and $$x,y,z$$ satisfy

$x^{11}+y^{11}=z^{11},$

then the number of ordered triples $$(x,y,z)$$ is $$n$$.

If the smallest positive integer $$k$$ satisfies the congruence $$n\cdot k \equiv 4 \pmod{11},$$ what is the value of $$n+k$$ ?

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