Math is radical 2

Algebra Level 5

Consider the following equation 1+2+3+6=a+b+c+d 1+\sqrt{2}+\sqrt{3}+\sqrt{6}=\sqrt{a+\sqrt{b+\sqrt{c+\sqrt{d}}}} where a,b,c,d\large\color{blue}{a,b,c,d} are integers. Find a+b+c+d\large\color{blue}{a+b+c+d}.

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