Let \( f: R \rightarrow R \) be a function defined as \(f(x)=\left\{\begin{array}{cc}\frac{\sin (a+1) x+\sin 2 x}{2 x}, …

Let \( f: R \rightarrow R \) be a function defined as

\(f(x)=\left\{\begin{array}{cc}\frac{\sin (a+1) x+\sin 2 x}{2 x}, & \text { if } x<0 \\b & , \text { if } x=0 \\\frac{\sqrt{x+b x^{3}}-\sqrt{x}}{b x^{5 / 2}} & , \text { if } x>0\end{array}\right.\)

If \( f \) is continuous at \( x=0 \), then the value of \( a+b \) is equal to

[JEE Main 2021, 18 Mar (Shift 2)]