Why is the ratio maximum range speed/maximum endurance speed the same for any airplane?
The ratio is the same for all aeroplanes if you accept a number of assumptions:

The propulsion efficiency is constant, regardless of speed or power setting
Aerodynamic drag is the sum of parasite drag and induced drag
Parasite drag is proportional to the square of airspeed:$ D_p = k_p \cdot V^2$
Induced drag is inversely proportional to the square of airspeed: $D_i = \frac{k_i }{V^2}$
There is no wind

Since we assume the propulsion efficiency is constant, the fuel consumption rate is directly proportional to the power required. The power required is drag times airspeed:
$P = D\cdot V = D_p\cdot V + D_i\cdot V = k_p\cdot V^3 + \frac{k_i}{V}$
For the maximum endurance we need to minimise the fuel consumption and thus we need to find the speed that minimises the power.
$\frac{dP}{dV} = 3 k_p V^2 - \frac{k_i}{V^2} = 0$
Solving for $V$ results in
$V_{endurance} =  \sqrt[\uproot{1}4]{   \frac{k_i}{3k_p}} $
For the maximum range we need to find the speed that minimises the fuel consumption per distance travelled, which is found when the ratio of power to  speed over ground is minimal. As we assume there is no wind, the ground speed and the airspeed are equal.  Since the ratio of power to airspeed is drag, we have to find the speed for minimum drag:
$\frac{dD}{dV} = 2 k_p V - 2\frac{k_i}{V^3} = 0$
Solving for $V$ results in
$V_{range} =   \sqrt[\uproot{1}4]{   \frac{k_i}{k_p}} $
We can now show that the ratio of maximum range speed to maximum endurance speed is:
$\frac{V_{range}}{V_{endurance}} = \left. \sqrt[\uproot{1}4]{   \frac{k_i}{k_p}} \middle/  \sqrt[\uproot{1}4]{\frac{k_i}{3k_p}} \right. = \left. 1 \middle/  \sqrt[\uproot{1}4]{\frac{1}{3}} \right. =  \sqrt[\uproot{1}4]{ 3} = 1.316... $

Now as long as the assumptions hold, for any aircraft the ratio of the speed will be approximately 1.3.
For the F-35 the ratio may be approximately right in the subsonic domain. Effects of compressibility will cause the drag to be higher when the aircraft gets into the transonic domain so depending on the max-range speed the last two assumptions may not hold.
For an autogyro at higher speeds, the relation of induced drag to airspeed is inversely proportional to the square of velocity, just like conventional fixed wing aircraft. This is because the fundamental way of creating lift by deflecting the incoming airflow downwards is the same for autogyros and aeroplanes. Therefore autogyros have also a factor pf approximately 1.3 between their maximum endurance and maximum range speeds.