Let \; f:\mathbb{R}\to\mathbb{R} \text{ be defined as} \[ f(x) = \begin{cases} \dfrac{\sin\!\big((a+1)x\big)+\sin 2x}{2x}, & x<0 \\[8pt] b, & x=0 \\[8pt] \dfrac{\sqrt{x+bx^{3}}-\sqrt{x}}{b\,x^{5/2}}, & x>0 \end{cases} \] If f is continuous at x = 0, then the value of a + b is equal to :