Math is radical 2

Algebra Level 4

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

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