Dimca's conjecture on the Tjurina number of reducible plane curves

Let $C=C_J\cup C_K$ be a reducible plane curve with the notation used above, where $C_J$ and $C_K$ are the corresponding subcurves and $\textup{I}(C_J,C_K)$ denotes their intersection number. Write $\tau(C)$ for the Tjurina number of $C$. Dimca's conjecture. With the previous notation one has

$$\tau(C)\leq\tau(C_J)+\tau(C_K)+2\cdot \textup{I}(C_J,C_K)-1.$$

This conjecture concerns an upper bound for the Tjurina number of a reducible plane curve in terms of the Tjurina numbers of its subcurves and their intersection number. The source presents it as a conjecture of A. Dimca; its resolution status is not specified here.