Will you square ???

Algebra Level 4

If $$\sqrt { \sqrt { 3-\sqrt { 8 } } +\sqrt { 6+\sqrt { 32 } } } =\sqrt { \sqrt { a+b\sqrt { c } } }$$ ,where $$a,b,c\in$$natural numbers and $$c$$ is square free.Find $$a+b+c$$.

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