Notice that there are 6 terms of 6^x, therefore you may write the simplified equation such that:
6*6^x = 11
Use the property of exponentials: 6*6^x = 6^(1+x)
Write the equation: 6^(1+x) = 11
Using logarithmation yields:
ln(6^(1+x)) = ln11 => (1+x)ln6 = ln11
ln 6 + xln6 = ln11
Subtracting ln 6 both sides yields: xln6 = ln 11 - ln 6
xln6 = ln(11/6) => x = ln(11/6)/ln 6
The solution to the given exponential equation is x = ln(11/6)/ln 6.
Considering 6^x +6^x +6^x +6^x +6^x 6^x =11,
this is a quadratic equation in 6^x. but it will have imaginary roots so this will not be posssible.
if it is 6^x +6^x +6^x +6^x +6^x +6^x=11
thus x=logarithm of 11/6 to the base 6
x=0.33829082295831 [using online log calculator]