Unknown powers 2

Let a, b and c be three positive integers so that

\(a+b+c=19\\ \\ { a }^{ b }+{ b }^{ c }+{ c }^{ a }=1149201\)

Let

\(\frac { 1 }{ a } +\frac { 1 }{ b } +\frac { 1 }{ c } =\frac { x }{ y }\)

where x and y are positive coprime integers.

Find the value of x+y.

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