Supposing I write an algorithm that results into this kind of recurrence relation
$$\left\{ \begin{array}{ll} T(0)=T(1)=1 \\ T(n)=T\left(\lfloor n/2 \rfloor \right)+T\left(\lceil n/2 \rceil\right)+c_1n+c_2 \end{array} \right.$$
This kind of algorithm looks like it is of $O(n\log(n))$ but how can I solve this recurrence relation to find its complexity?