The $7/5$ cycle-cover conjecture for bridgeless graphs

Let $G$ be a bridgeless graph, not necessarily cubic, and let $E$ denote its edge set. A cycle cover here is a list of cycles in which every edge of $G$ lies on at least one cycle. $7/5$ cycle-cover conjecture. The graph $G$ has a list of cycles such that every edge lies on at least one of them and the sum of their lengths is at most

$$\frac{7}{5}\cdot |E|.$$

This is another classical conjecture listed as a consequence of the Petersen coloring conjecture. The source gives no evidence that it has been resolved.