Let \( \alpha=3\sin^{-1}\!\left(\dfrac{6}{11}\right) \) and \( \beta=3\cos^{-1}\!\left(\dfrac{4}{9}\right) \), where inverse trigonometric functions take only the principal values. Given below are two statements:
Statement-I: \( \cos(\alpha+\beta)>0 \).
Statement-II: \( \cos(\alpha)<0 \).
In the light of the above statements, choose the correct answer from the options given below:
