Nested floors and ceilings

Algebra Level 3

\[\sqrt{ \left \lceil \lfloor \sqrt{6} \rfloor \right \rceil +\sqrt{ \left \lceil \lfloor \sqrt{6} \rfloor \right \rceil + \sqrt{ \left \lceil \lfloor \sqrt{6} \rfloor \right \rceil + \sqrt{ \left \lceil \lfloor \sqrt{6} \rfloor \right \rceil + \cdots}}}} = \, ? \ \]

\[ \]

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