To sum it is to damp it

Algebra Level 3

\(If\quad a\sqrt { 2 } +b\sqrt { 3 } +c\sqrt { 6 } =\sqrt { 2009+918\sqrt { 2 } +272\sqrt { 3 } +72\sqrt { 6 } } \\and\quad a,b,c\quad \in \quad { ℤ }^{ + }\quad \\ find\quad the\quad value\quad of\quad a+b+c\)

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