Let $$f : R \to R$$ be a function defined as
$$$f(x) = \begin{cases} \frac{\sin(a+1)x + \sin 2x}{2x}, & \text{if } x < 0 \\ b, & \text{if } x = 0 \\ \frac{\sqrt{x+bx^3} - \sqrt{x}}{bx^{5/2}}, & \text{if } x > 0 \end{cases}$$$
If $$f$$ is continuous at $$x = 0$$, then the value of $$a + b$$ is equal to :

A

$$-\frac{5}{2}$$

B

$$-2$$

C

$$-3$$

D

$$-\frac{3}{2}$$