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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