If \[\large{x^{2050}-a^{2050}+y^{2050}-b^{2050}+z^{2050}-c^{2050}=465893}\]

If above equation is true for some integers \((x,y,z,a,b,c)\) and the pair of solutions be \((x_{1},y_{1},z_{1},a_{1},b_{1},c_{1})\),...., \((x_{n},y_{n},z_{n},a_{n},b_{n},c_{n})\). Find the value of

\[\large{\sum _{ i=1 }^{ n }{ { x }_{ i }+{ y }_{ i }+{ z }_{ i }+{ a }_{ i }+{ b }_{ i }+{ c }_{ i } } }\]

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