Vector Algebra: JEE Main 2023 Mathematics question

If the vectors $\overrightarrow a = \lambda \widehat i + \mu \widehat j + 4\widehat k$, $\overrightarrow b = - 2\widehat i + 4\widehat j - 2\widehat k$ and $\overrightarrow c = 2\widehat i + 3\widehat j + \widehat k$ are coplanar and the projection of $\overrightarrow a$ on the vector $\overrightarrow b$ is $\sqrt {54}$ units, then the sum of all possible values of $\lambda + \mu$ is equal to :