If the two roots of the quadratic $3x^2+5x+k$ are $\frac{-5\pm i\sqrt{11}}{6}$, what is $k$?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
If the two roots of the quadratic $3x^2+5x+k$ are $\frac{-5\pm i\sqrt{11}}{6}$, what is $k$?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
3
If the two roots of the quadratic $3x^2+5x+k$ are $\frac{-5\pm i\sqrt{11}}{6}$, what is $k$?
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