Isn't the left side bigger?

4x+5y=3z \large { 4 }^{ x }+{ 5 }^{ y }={ 3 }^{ z }

For non-negative integers x,y,zx,y,z, let triplets {x1,y1,z1},{x2,y2,z2}{xn,yn,zn}\left\{ { x }_{ 1 },{ y }_{ 1 },{ z }_{ 1 } \right\} ,\left\{ { x }_{ 2 },{ y }_{ 2 },{ z }_{ 2 } \right\} \ldots \left\{ { x }_{ n },{ y }_{ n },{ z }_{ n } \right\} be the solutions to the equation above,

Submit your answer as i=1n(xi+yi+zi)\displaystyle \sum _{ i=1 }^{ n }( { { x }_{ i }+{ y }_{ i }+{ z }_{ i } } ).

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