Video solution:

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Written solution:

The first statement means $$3n^2 + 2n+d = 263.$$

Similarly, the second statement means $$3n^2 +2n +4$$$$= 6^3 +6^2 +6d+1$$$$= 253 + 6d.$$

Subtracting these shows us that $$4-d = 6d-10$$ $$7d = 14$$ $$d=2.$$ Therefore, $3n^2 + 2n + 2 = 263,$ so $n(3n+2) = 261.$

This implies $n=9.$ Therefore, $n+d = 11.$

Thus, the answer is B .