If $C$ is a circle of radius 7 centered at the point $(-2,-4)$, then evaluate \[ \oint_{C}\left(3 y-e^{\sin (x)}\right) d x+\left(9 x-\sin \left(y^{3}+y\right)\right) d y \text {. } \] value $=$

Step 1 ：The given integral is a line integral over a closed curve. By Green's theorem, this can be converted into a double integral over the region enclosed by the curve.

Step 2 ：However, the integrand is not a conservative vector field, so we cannot use the fundamental theorem of line integrals to simplify the integral to a difference of potential functions at two points.

Step 3 ：We can notice that the curve is a circle, and the integrand does not depend on the path, only on the endpoints. Since the curve is closed, the endpoints coincide, and the integral over the curve should be zero.

Step 4 ：Therefore, the value of the line integral over the closed curve \(C\) is \(\boxed{0}\).