Self-destructive it is!

Calculus Level 4

\[\sum _{ x=0 }^{ \infty } \frac { \left( 2x \right) !\left( { { 1 }^{ x }+2^{ x }+{ 3 }^{ x }+{ 4 }^{ x }+5 }^{ x }+6^{ x } \right) }{ { x! }^{ 2 }{ 60 }^{ x } }\]

If the sum above can be written in the form \[\sqrt { 15 } \left( \frac { 1 }{ \sqrt { a } } +\frac { 1 }{ \sqrt { b } } +\frac { 1 }{ \sqrt { c } } \right) +\sqrt { 5 } \left( \frac { 1 }{ 2 } +\frac { 1 }{ \sqrt { d } } \right) +\sqrt { \frac { 3 }{ 2 } }, \]

then find \({ \left( a+b+c+d \right) }^{ 2 }\).

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