The equation given is,
[tex]\left|6x-10\:\right|=\left|5x+6\right|[/tex]
Find the positive and the negative intervals
[tex]x<-\frac{6}{5},\:\:-\frac{6}{5}\le \:x<\frac{5}{3},\:\:x\ge \frac{5}{3}[/tex]
Solve the inequality for each intervals
[tex]\begin{gathered} \mathrm{No\:Solution}\quad \mathrm{or}\quad \:x=\frac{4}{11}\quad \mathrm{or}\quad \:x=16 \\ x=\frac{4}{11}\quad \mathrm{or}\quad \:x=16 \end{gathered}[/tex]
Hence, the answer is
[tex]x=\frac{4}{11}\quad\mathrm{or}\quad\:x=16\text{ \lparen Two solutions\rparen}[/tex]
