Root 11 to the infinity

Algebra Level 2

11+11+11+11+11\large \sqrt{\color{#624F41}{11} + \sqrt {\color{#302B94}{11} + \sqrt{\color{#20A900}{11} + \sqrt {\color{#EC7300}{11} + \sqrt {\color{#E81990}{11} \ldots }}}}}

What is the value of the expression above? Round your answer off to nearest whole number.

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