Algebra Level pending

Have you been studying for your LAT's? Well, this shall decide whether you join the club or not. Let's go!

If

$$\begin{cases} \log _{ x+a }{ x } \le \log_{a}{x^2},a>0,a\neq 1 \\ \frac { 2+\log_{3}{y} }{ y-1 } <\frac { 6}{ 2y-1 } \end{cases}$$

and

$$x>L$$ when $$a>1$$; $$U<x\le \sqrt { a}-a$$ and $$M-a<x\le B$$ when $$0<a<1$$,

and

$$E \le y \le R$$,

evaluate

$$L+U+M+B+E+R$$

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