Let \([t]\) denote the largest integer less than or equal to \( t \). If \( \displaystyle \int_{0}^{3}\Big(\,[x^{2}] + \Big[\dfrac{x^{2}}{2}\Big] \,\Big)dx = a + b\sqrt{2} - \sqrt{3} - \sqrt{5} + c\sqrt{6} - \sqrt{7} \), where then \( a,b,c \in \mathbb{Z} \), then \( a+b+c \) is equal to ______.
