$\large \lim_{n\to\infty} \dfrac{ \lceil x \rceil + \lceil 2x \rceil + \lceil 3x \rceil + \cdots + \lceil n x \rceil }{n^2}$

Let $a,b,x$ be constants such that the limit above can be expressed as $ax + b$.

Find the value of $a^2+b^2$.

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