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How to compare these two numbers without using a calculator ?

$A=\left(\dfrac{11}{10}\right)^{\sqrt{5}}$ and $\;B=\left(\dfrac{12}{11}\right)^{\sqrt{6}}$.

Thanks for your help !

Here is what I tried for example : $$\left(\frac{A}{B}\right)^{\sqrt6-\sqrt5}=\frac{11}{10^{\sqrt{30}−5}12^{6−\sqrt{30}}}.$$

ln is concave, so $$10^{\sqrt{30}−5}12^{6−\sqrt{30}}\leq10(\sqrt{30}−5))+12(6−\sqrt{30})=22−2\sqrt{30}.$$ But $$22−2\sqrt{30}\approx11,05...$$